$A$ $B$ $C$ If: $ AB = 4x + 3$, $ AC = 53$, and $ BC = 8x + 2$, Find $BC$.
From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {4x + 3} + {8x + 2} = {53}$ Combine like terms: $ 12x + 5 = {53}$ Subtract $5$ from both sides: $ 12x = 48$ Divide both sides by $12$ to find $x$ $ x = 4$ Substitute $4$ for $x$ in the expression that was given for $BC$ $ BC = 8({4}) + 2$ Simplify: $ {BC = 32 + 2}$ Simplify to find ${BC}$ : $ {BC = 34}$